Now showing items 11-20 of 78
Diophantine and Ergodic Foliations on Surfaces
(Oxford University Press, 2012-11-16)
The Evolution of Geometric Structures on 3-Manifolds
(American Mathematical Society, 2011)
This paper gives an overview of the geometrization conjecture and approaches to its proof.
Entropy on Riemann Surfaces and the Jacobians of Finite Covers
(European Mathematical Society, 2012-11-16)
This paper characterizes those pseudo-Anosov mappings whose entropy can be detected homologically by taking a limit over finite covers. The proof is via complex-analytic methods. The same methods show the natural map ...
K3 Surfaces, Entropy and Glue
(Walter de Gruyter, 2011)
Hausdorff Dimension and Conformal Dynamics III: Computation of Dimension
(Johns Hopkins University Press, 1998)
This paper presents an eigenvalue algorithm for accurately computing the Hausdorff dimension of limit sets of Kleinian groups and Julia sets of rational maps. The algorithm is applied to Schottky groups, quadratic polynomials ...
Self-Similarity of Siegel Disks and Hausdorff Dimension of Julia Sets
(Springer Netherlands, 1998)
Let f(z) = e2 i z +z2, where θ is an irrational number of bounded type. According to Siegel, f is linearizable on a disk containing the origin. In this paper we show: • the Hausdorff dimension of the Julia set J(f) is ...
The Classification of Conformal Dynamical Systems
(International Press, 1995)
Hausdorff Dimension and Conformal Dynamics II: Geometrically Finite Rational Maps
(Birkhäuser Basel, 2000)
This paper investigates several dynamically defined dimensions for rational maps \(f\) on the Riemann sphere, providing a systematic treatment modeled on the theory for Kleinian groups. We begin by defining the radial Julia ...
Trees and the Dynamics of Polynomials
(Societe Mathematique de France, 2008)
In this paper we study branched coverings of metrized, simplicial trees F : T → T which arise from polynomial maps f : C → C with disconnected Julia sets. We show that the collection of all such trees, up to scale, forms ...
Thermodynamics, Dimension and the Weil-Petersson Metric
(Springer Verlag, 2008)